# Distributive and the Amazing Math Maze

012A

Welcome to distributive and the Amazing Math Maze. So, either you missed Question 12 of the aMazing Math Maze of you found this page doing a search for the distributive law. I would love to tell you about the aMazing Math Maze which was built for Algebra 1 students - but first I would like to talk about question 12. There are people doing really well with the Maze that have missed Question 12 and we are about to tell them why - and give them another shot at it.

## Question 12 of the aMazing Math Maze

If you'll recall the question looked like this -

3x(x^{4}+ x - 3)

a) 3x^{4} + 4x – 3

b) 3x^{5} + x – 3

c) 3x

^{5} + 3x – 9

d) 3x^{5} + 3x^{2} - 9x

And, I mentioned that we would be using the distributive property. By this I meant that we would multiply each term in the parentheses by the term outside the parentheses. So each item gets multiplied by 3x.

In answer A we multiplied the first term by 3 but not by x. It should have raised the exponent to 5.

In answer B we multiplied the first term by 3x but not the second or third.

In answer C we were correct in the first term, but failed to multiply the second or third term by the x.

Answer D was the correct answer.

## The Distributive Property

In the above example I used arrows to show what the term outside the parenthesis gets multiplied times. 6x squared first gets multiplied times the 3x cubed, and we get 18 x to the fifth. 6 times 3 is 18 and x squared times x to the third is x to the 5th. The purple arrow shows the next multiplication resulting in negative 12 x to the fourth, then the brown arrow ends up being 24 x squared. Note that we leave the negative 2x alone - it' not in the parenthesis. And the whole mess equals 5. If you like worksheets (and who doesn't?) **Kutra Software** is a good resource. Keeping in mind, I am accepting no remuneration from them (mostly because it hasn't been offered). Anyway, if you have any comments about their service, I am very curious as to your experience. Please write me a note using the form at the bottom of this page - thanks.

## The new Problem 12a

2x^{2}(x^{3}+ 6) -7

a) 2x^{5} + 12x^{2} – 7

b) 3x^{5} + 12x – 7

c) 2x

^{5} + 12x

^{2} – 14x

^{2}
d) 2x^{5} - 2x^{2}

Click a letter corresponding to the most correct answer of the expression.

**a) ****b)** **c) ****d)**